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An isosceles right triangle and a square have the same area. If the length of the hypotenuse of the right triangle is 6 √ 2, what is the area of the square?

f) 12
g) 12+6 √ 2
h) 18
j) 24+6 √ 2
k) 36

User Chatax
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2 Answers

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An isosceles right triangle is a 45°-45°-90° triangle. 45°-45°-90° triangles' hypotenuses are always equal to their leg length times the square root of two.


For 45°-45°-90° triangles:


Leg = x

Hypotenuse = x√(2)


The length of the hypotenuse is given (6√(2)), so we can easily find the length of its legs. If we divide the hypotenuse by √(2), we are left with 6. This is the leg length.


To find the area of the triangle (and thus the area of the square), use the formula for area of a triangle, A = bh/2. Our b, base, is 6, and our h, height, is also 6. Plug these values in accordingly and solve.


A = 6 * 6/2

A = 36/2

A = 18


The area of the triangle (and that of the square) is 18 units squared.


Answer:

The area of the square is 18 units².

h) 18
User Mamboking
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3 votes

Isosceles right triangles are a special right triangle because it follows the 45-45-90 rule. If one leg was x, then the other leg was also x and the hypotenuse was x√2.


Using that information, we can confirm that the legs of the triangle are 2 since 6√2 divided by √2 is 6.


Now that we have the legs of the triangle, we can use the formula for the area of the triangle to solve: (remember that area = (bh)/2)



A=(6*6)/(2)


Firstly, multiply the numerator:
A=(36)/(2)


Next, divide, and your answer will be A = 18. Since the square and the right triangle have the same area, your answer is 18, or h.

User Jan Gabriel
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7.8k points

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